Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac{A \cdot STDAGE_{t2}}{k+STDAGE_{t2}}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the peak growing season (June-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1960-1989), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Model selection is used to determine the best fitting models, which is implemented in two parts. The first part selected the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).

model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

model 3: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

sub-model b: s form \(\left( \frac {A \cdot STDAGE_{t2}^s} {k^s+STDAGE_{t2}^s} \right)\)

sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot STDAGE_{t2}^s} {k^s + STDAGE_{t1}^s} \right)\)

Note:

This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval

This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):

exclude FIA plots in plantation forests
exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   6803     1682.7                                
## 2   6802     1681.9  1   0.817   3.3024 0.06922 .  
## 3   6801     1508.3  1 173.521 782.3941 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 73664.85
## 2     2 73663.54
## 3     3 72924.43

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.224e-01  1.983e-01    2.13   0.0332 *  
## phi   9.657e-03  6.353e-03    1.52   0.1286    
## alpha 8.551e-01  2.782e-02   30.73   <2e-16 ***
## A     4.130e+02  2.663e+01   15.51   <2e-16 ***
## k     1.748e+02  1.210e+01   14.44   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4709 on 6801 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.741e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   6801     1508.3                             
## 2   6800     1507.4  1 0.96192  4.3394 0.03728 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 72924.43
## 2    3a 72922.09
## 3    3b       NA
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.372e-01  1.995e-01   2.192   0.0284 *  
## phi   9.948e-03  6.376e-03   1.560   0.1188    
## alpha 8.524e-01  2.770e-02  30.769  < 2e-16 ***
## A     4.689e+02  5.544e+01   8.458  < 2e-16 ***
## k     2.195e+02  3.752e+01   5.849 5.16e-09 ***
## p     1.022e-02  4.649e-03   2.198   0.0280 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4708 on 6800 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 8.162e-06

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 292 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 292 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 67 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1  18749     6338.2                               
## 2  18744     6337.9  5   0.261   0.1545 0.9787    
## 3  18743     6070.3  1 267.554 826.1114 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 195514.5
## 2     2 195475.2
## 3     3 194668.6

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.353588   0.110897   3.188  0.00143 ** 
## phi    -0.001996   0.003688  -0.541  0.58844    
## alpha   0.737003   0.023797  30.971  < 2e-16 ***
## A     179.312279   5.156726  34.773  < 2e-16 ***
## k      69.228552   2.165126  31.974  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5691 on 18743 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.228e-06
##   (27 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  18743     6070.3                                
## 2  18742     6024.5  1 45.811  142.52 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 194668.6
## 2    3a 194528.5
## 3    3b 194664.1
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.306503   0.108473   2.826  0.00472 ** 
## phi    -0.001440   0.003674  -0.392  0.69515    
## alpha   0.721462   0.021813  33.074  < 2e-16 ***
## A     220.082506   9.814957  22.423  < 2e-16 ***
## k     112.272660   7.835130  14.329  < 2e-16 ***
## p       0.039500   0.002695  14.655  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.567 on 18742 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 7.397e-06
##   (27 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 709 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 709 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 140 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   7166     1248.9                             
## 2   7165     1248.8  1   0.09  0.5136 0.4736    
## 3   7156     1115.0  9 133.80 95.4108 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 78262.17
## 2     2 78263.66
## 3     3 77388.99

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.177767   0.125695   1.414    0.157    
## phi    -0.003182   0.004610  -0.690    0.490    
## alpha   0.833125   0.026621  31.295   <2e-16 ***
## A     471.875581  24.383587  19.352   <2e-16 ***
## k     142.228754   8.530248  16.673   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3947 on 7156 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.873e-06
##   (9 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   7156     1115.0                          
## 2   7155     1114.7  1 0.32532  2.0881 0.1485
##   model      AIC
## 1     3 77388.99
## 2    3a 77388.90
## 3    3b 77366.35
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.230108   0.128881   1.785   0.0742 .  
## phi    -0.003611   0.004596  -0.786   0.4321    
## alpha   0.841062   0.026798  31.385   <2e-16 ***
## A     307.335491  21.963531  13.993   <2e-16 ***
## k      68.630153   7.052532   9.731   <2e-16 ***
## s       1.252251   0.052561  23.825   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3941 on 7155 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.799e-06
##   (9 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 214 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 214 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 95 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   4870     1492.4                              
## 2   4869     1491.8  1   0.593  1.9356 0.1642    
## 3   4862     1388.0  7 103.773 51.9275 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 52508.96
## 2     2 52509.02
## 3     3 52116.67

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.108312   0.201218  -0.538    0.590    
## phi     0.021351   0.009589   2.227    0.026 *  
## alpha   0.875306   0.042046  20.818   <2e-16 ***
## A     450.989851  38.681653  11.659   <2e-16 ***
## k     187.931256  18.156596  10.351   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5343 on 4862 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.47e-06
##   (10 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   4862     1388.0                            
## 2   4861     1386.8  1 1.2116  4.2469 0.03938 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 52116.67
## 2    3a 52114.42
## 3    3b       NA
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.086726   0.203625  -0.426   0.6702    
## phi     0.021015   0.009581   2.193   0.0283 *  
## alpha   0.885443   0.042244  20.960  < 2e-16 ***
## A     396.339480  42.136289   9.406  < 2e-16 ***
## k     150.640293  23.061134   6.532 7.14e-11 ***
## p      -0.011878   0.007526  -1.578   0.1145    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5341 on 4861 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.24e-06
##   (10 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95924, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -31.565, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 160 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 160 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 57 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1   8773     1635.6                                  
## 2   8772     1634.2  1   1.345   7.2189  0.007228 ** 
## 3   8768     1511.6  4 122.662 177.8789 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 92156.63
## 2     2 92151.41
## 3     3 91445.87

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.211037   0.117857   1.791  0.07339 .  
## phi    -0.015961   0.005137  -3.107  0.00189 ** 
## alpha   0.776341   0.027255  28.484  < 2e-16 ***
## A     246.896440   9.049774  27.282  < 2e-16 ***
## k      72.053158   3.462078  20.812  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4152 on 8768 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.748e-06
##   (10 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   8768     1511.6                           
## 2   8767     1511.5  1 0.028753  0.1668  0.683
##   model      AIC
## 1     3 91445.87
## 2    3a 91447.70
## 3    3b 91417.00
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.222553   0.118311   1.881  0.05999 .  
## phi    -0.015283   0.005127  -2.981  0.00288 ** 
## alpha   0.780966   0.027354  28.550  < 2e-16 ***
## A     181.122164   8.521131  21.256  < 2e-16 ***
## k      40.816766   2.670898  15.282  < 2e-16 ***
## s       1.356136   0.063516  21.351  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4145 on 8767 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.465e-06
##   (10 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 275 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 275 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 44 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1  12328     3402.9                                
## 2  12327     3401.7  1   1.174   4.2556 0.03914 *  
## 3  12326     3168.4  1 233.379 907.9214 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 134092.1
## 2     2 134089.8
## 3     3 133215.4

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.352889   0.136159   9.936   <2e-16 ***
## phi    -0.009457   0.004513  -2.096   0.0361 *  
## alpha   0.625058   0.019024  32.855   <2e-16 ***
## A     228.475174   7.054443  32.387   <2e-16 ***
## k      54.645649   1.681040  32.507   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.507 on 12326 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.105e-06
##   (16 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  12326     3168.4                                 
## 2  12325     3071.9  1  96.516  387.24 < 2.2e-16 ***
## 3  12325     3133.0  0   0.000                      
## 4  12324     2996.0  1 137.008  563.58 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 133215.4
## 2    3a 132836.0
## 3    3b 133079.1
## 4    3c 132529.7

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.823084   0.153940  11.843  < 2e-16 ***
## phi    -0.012617   0.004372  -2.886  0.00391 ** 
## alpha   0.724875   0.014206  51.027  < 2e-16 ***
## A     136.610805   4.469965  30.562  < 2e-16 ***
## k      32.316058   0.886557  36.451  < 2e-16 ***
## p       0.176183   0.007462  23.610  < 2e-16 ***
## s       2.205140   0.091515  24.096  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4931 on 12324 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 8.858e-06
##   (16 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 382 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 382 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 68 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1  12427     5120.9                                  
## 2  12426     5118.1  1   2.827   6.8637  0.008807 ** 
## 3  12425     4833.3  1 284.863 732.3053 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 138056.4
## 2     2 138051.6
## 3     3 137341.7

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    8.572e-01  1.436e-01   5.969 2.45e-09 ***
## phi   1.414e-02  5.721e-03   2.472   0.0135 *  
## alpha 6.367e-01  2.131e-02  29.881  < 2e-16 ***
## A     2.328e+02  8.568e+00  27.167  < 2e-16 ***
## k     5.338e+01  2.004e+00  26.642  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6237 on 12425 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.379e-06
##   (40 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_232,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  12425     4833.3                                 
## 2  12424     4689.0  1 144.248  382.20 < 2.2e-16 ***
## 3  12423     4615.3  1  73.722  198.44 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 137341.7
## 2    3a 136967.1
## 3    3b       NA
## 4    3c 136772.1

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.090e+00  1.503e-01   7.253 4.31e-13 ***
## phi   1.466e-02  5.562e-03   2.636  0.00839 ** 
## alpha 7.472e-01  1.529e-02  48.872  < 2e-16 ***
## A     1.517e+02  5.942e+00  25.527  < 2e-16 ***
## k     3.507e+01  1.268e+00  27.655  < 2e-16 ***
## p     1.838e-01  9.439e-03  19.475  < 2e-16 ***
## s     2.151e+00  1.096e-01  19.632  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6095 on 12423 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 6.557e-06
##   (40 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 459 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 459 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 84 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   1260     341.40                              
## 2   1259     340.98  1  0.414   1.5275 0.2167    
## 3   1258     304.55  1 36.436 150.5075 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14064.19
## 2     2 14064.66
## 3     3 13923.93

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.03235    0.38674  -0.084    0.933    
## phi     0.02239    0.01919   1.167    0.243    
## alpha   0.76482    0.05648  13.542  < 2e-16 ***
## A     534.76505   90.58922   5.903 4.58e-09 ***
## k     150.62413   29.17636   5.163 2.83e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.492 on 1258 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.796e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1258     304.55                          
## 2   1257     303.96  1 0.58527  2.4203   0.12
##   model      AIC
## 1     3 13923.93
## 2    3a 13923.50
## 3    3b       NA
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.068800   0.379721  -0.181  0.85625    
## phi     0.024165   0.019198   1.259  0.20837    
## alpha   0.756814   0.056010  13.512  < 2e-16 ***
## A     914.887761 480.230226   1.905  0.05699 .  
## k     324.181993 213.143210   1.521  0.12852    
## p       0.012477   0.004042   3.087  0.00207 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4917 on 1257 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.186e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96021, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.162, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 34 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 34 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 29 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in nls(f_1, data = G_242, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(f_2, data = G_242, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(f_3, data = G_242, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   1793     399.39                               
## 2   1792     399.38  1  0.0056   0.0253 0.8737    
## 3   1791     377.43  1 21.9521 104.1677 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18766.17
## 2     2 18768.15
## 3     3 18668.61

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.208773   0.327252   0.638    0.524    
## phi    -0.003168   0.012502  -0.253    0.800    
## alpha   0.750699   0.068278  10.995   <2e-16 ***
## A     277.874870  28.834628   9.637   <2e-16 ***
## k     106.568383  12.736078   8.367   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4591 on 1791 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.734e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   1791     377.43                             
## 2   1790     376.81  1 0.62625   2.975 0.08473 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 18668.61
## 2    3a 18667.63
## 3    3b 18645.17
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.23065    0.32840   0.702    0.483    
## phi    -0.00104    0.01255  -0.083    0.934    
## alpha   0.76426    0.06853  11.153   <2e-16 ***
## A     149.64370   13.42374  11.148   <2e-16 ***
## k      38.36509    3.00470  12.768   <2e-16 ***
## s       1.82807    0.16802  10.880   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4559 on 1790 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.976e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96947, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.321, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 60 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 60 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 55 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    658     209.60                                
## 2    657     209.57  1  0.023   0.072    0.7885    
## 3    656     190.82  1 18.755  64.477 4.528e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6702.388
## 2     2 6704.315
## 3     3 6644.344

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.09785    0.39859  -0.245    0.806    
## phi    -0.04344    0.02679  -1.622    0.105    
## alpha   0.77374    0.08594   9.003  < 2e-16 ***
## A     191.05053   26.63609   7.173 1.99e-12 ***
## k      54.86848    9.52757   5.759 1.30e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5393 on 656 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.699e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    656     190.82                           
## 2    655     190.80  1 0.018429  0.0633 0.8015
##   model      AIC
## 1     3 6644.344
## 2    3a 6646.280
## 3    3b 6640.117
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.15197    0.38750  -0.392   0.6951    
## phi    -0.04738    0.02660  -1.781   0.0754 .  
## alpha   0.80479    0.08649   9.305  < 2e-16 ***
## A     122.71846   16.14074   7.603 1.01e-13 ***
## k      23.86754    3.54344   6.736 3.57e-11 ***
## s       1.65406    0.24745   6.685 4.96e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5372 on 655 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 7.623e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94016, p-value = 1.183e-15
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.6852, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1     20     3.4359                           
## 2     19     3.4302  1 0.005736  0.0318 0.8604
## 3     18     3.1869  1 0.243212  1.3737 0.2565
##   model      AIC
## 1     1 308.6562
## 2     2 310.6177
## 3     3 310.9262

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   -2.726      0.354  -7.701 2.09e-07 ***
## A  8572.749   9212.429   0.931    0.363    
## k   717.133    829.205   0.865    0.397    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4145 on 20 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 9.519e-07
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1     20     3.4359                             
## 2     19     3.4358  1 5.6057e-05   3e-04 0.9861
##   model      AIC
## 1     1 308.6562
## 2    1a 310.6558
## 3    1b 310.6552
## 4    1c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   -2.726      0.354  -7.701 2.09e-07 ***
## A  8572.749   9212.429   0.931    0.363    
## k   717.133    829.205   0.865    0.397    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4145 on 20 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 9.519e-07
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit
unable to fit model (only 64 observations)

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96671, p-value = 0.6107
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.1715, p-value = 0.2414
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 2 rows containing missing values (geom_segment).

## Warning: Removed 275 row(s) containing missing values (geom_path).

plotting 2

## Warning: Removed 1 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 2 rows containing missing values (geom_segment).

262 - California Dry Steppe

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_262.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    151     26.657                                 
## 2    150     26.628  1 0.02844  0.1602 0.6895331    
## 3    149     24.403  1 2.22523 13.5869 0.0003183 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1931.239
## 2     2 1933.074
## 3     3 1921.635

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge       0.45026    1.56137   0.288 0.773458    
## phi     -0.03686    0.06427  -0.573 0.567172    
## alpha    0.90066    0.22752   3.959 0.000116 ***
## A     1723.50465  754.16358   2.285 0.023705 *  
## k      330.70576   96.49416   3.427 0.000788 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4047 on 149 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.76e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_263,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    149     24.403                           
## 2    148     24.330  1 0.073144  0.4449 0.5058
##   model      AIC
## 1     3 1921.635
## 2    3a 1923.173
## 3    3b 1923.633
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge       0.45026    1.56137   0.288 0.773458    
## phi     -0.03686    0.06427  -0.573 0.567172    
## alpha    0.90066    0.22752   3.959 0.000116 ***
## A     1723.50465  754.16358   2.285 0.023705 *  
## k      330.70576   96.49416   3.427 0.000788 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4047 on 149 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.76e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9769, p-value = 0.01083
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.8959, p-value = 0.05798
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    211     66.388                           
## 2    210     66.383  1 0.005176  0.0164 0.8983
## 3    209     66.150  1 0.232699  0.7352 0.3922
##   model      AIC
## 1     1 2297.872
## 2     2 2299.855
## 3     3 2301.104

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge  -0.9053     0.9254  -0.978   0.3291  
## A  293.7335   118.6877   2.475   0.0141 *
## k  168.8293    74.2410   2.274   0.0240 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5609 on 211 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 3.537e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    211     66.388                           
## 2    210     66.366  1 0.021814   0.069  0.793
##   model      AIC
## 1     1 2297.872
## 2    1a 2299.801
## 3    1b       NA
## 4    1c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge  -0.9053     0.9254  -0.978   0.3291  
## A  293.7335   118.6877   2.475   0.0141 *
## k  168.8293    74.2410   2.274   0.0240 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5609 on 211 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 3.537e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91405, p-value = 8.398e-10
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.328, p-value = 0.1842
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 8 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 8 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 81 row(s) containing missing values (geom_path).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in nls(f_1, data = G_322, start = c(ge = ge.start, A = A.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

Cannot fit model
not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    300     169.49                                 
## 2    299     157.71  1 11.7794 22.3326 3.534e-06 ***
## 3    298     155.97  1  1.7346  3.3141   0.06969 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3097.199
## 2     2 3077.373
## 3     3 3076.022

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     5.57640    6.13672   0.909   0.3642    
## phi   -0.11573    0.02054  -5.633 4.09e-08 ***
## alpha  0.46057    0.24332   1.893   0.0593 .  
## A     35.68667   22.88602   1.559   0.1200    
## k     23.38590    9.59842   2.436   0.0154 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7235 on 298 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 7.166e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_331,  : 
##   parameters without starting value in 'data': ge
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_331,  : 
##   parameters without starting value in 'data': ge
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_331,  : 
##   parameters without starting value in 'data': ge
##   model      AIC
## 1     3 3076.022
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     5.57640    6.13672   0.909   0.3642    
## phi   -0.11573    0.02054  -5.633 4.09e-08 ***
## alpha  0.46057    0.24332   1.893   0.0593 .  
## A     35.68667   22.88602   1.559   0.1200    
## k     23.38590    9.59842   2.436   0.0154 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7235 on 298 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 7.166e-06
##   (1 observation deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90559, p-value = 7.773e-13
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.4891, p-value = 7.152e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    191     97.286                             
## 2    190     97.242  1 0.04356  0.0851 0.77079  
## 3    189     94.642  1 2.60066  5.1935 0.02379 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2085.408
## 2     2 2087.321
## 3     3 2084.062

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## ge      0.35442    1.80312   0.197   0.8444  
## phi     0.01096    0.05265   0.208   0.8353  
## alpha   0.73232    0.29037   2.522   0.0125 *
## A     280.40101  204.47827   1.371   0.1719  
## k     166.97985  140.70361   1.187   0.2368  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7076 on 189 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.702e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    189     94.642                         
## 2    187     92.984  2 1.6575  1.6666 0.1917
##   model      AIC
## 1     3 2084.062
## 2    3a       NA
## 3    3b       NA
## 4    3c 2084.635

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## ge      0.35442    1.80312   0.197   0.8444  
## phi     0.01096    0.05265   0.208   0.8353  
## alpha   0.73232    0.29037   2.522   0.0125 *
## A     280.40101  204.47827   1.371   0.1719  
## k     166.97985  140.70361   1.187   0.2368  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7076 on 189 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.702e-06
##   (1 observation deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87017, p-value = 7.517e-12
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.5075, p-value = 3.639e-08
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    117     78.061                         
## 2    116     77.624  1 0.4369  0.6529 0.4207
## 3    109     73.777  7 3.8472  0.8120 0.5792
##   model      AIC
## 1     1 1267.796
## 2     2 1269.123
## 3     3 1207.774

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## ge    -1.63609    1.22318  -1.338   0.1838  
## phi   -0.01838    0.08470  -0.217   0.8286  
## alpha  0.63289    0.27137   2.332   0.0215 *
## A     81.82085   45.34337   1.804   0.0739 .
## k     -1.29940    1.48439  -0.875   0.3833  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8227 on 109 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 9.54e-06
##   (7 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    109     73.777                            
## 2    108     71.574  1 2.2026  3.3235 0.07106 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 1207.774
## 2    3a 1206.318
## 3    3b       NA
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.052537   1.909452  -0.551    0.583    
## phi   -0.009892   0.082404  -0.120    0.905    
## alpha  0.559295   0.288286   1.940    0.055 .  
## A     68.811869  46.891349   1.467    0.145    
## k     -8.039455   1.320643  -6.088 1.78e-08 ***
## p      1.218451   0.143912   8.467 1.38e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8141 on 108 degrees of freedom
## 
## Number of iterations to convergence: 20 
## Achieved convergence tolerance: 3.644e-06
##   (7 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90381, p-value = 5.439e-07
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.1984, p-value = 0.2308
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 4 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 81 row(s) containing missing values (geom_path).

plotting 2

411 - Everglades

model selection 1

## Error in nls(f_1, data = G_411, start = c(ge = ge.start, A = A.start,  : 
##   singular gradient
## Error in nls(f_2, data = G_411, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient
## Error in nls(f_3, data = G_411, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_411$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_411.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1   6723     1277.2                                  
## 2   6722     1270.9  1   6.306   33.355 8.021e-09 ***
## 3   6721     1093.8  1 177.024 1087.705 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 71147.96
## 2     2 71116.66
## 3     3 70109.75

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.631e-01  1.559e-01   2.971  0.00298 ** 
## phi   2.684e-02  5.634e-03   4.764 1.94e-06 ***
## alpha 8.139e-01  2.240e-02  36.331  < 2e-16 ***
## A     4.026e+02  2.188e+01  18.401  < 2e-16 ***
## k     1.738e+02  9.865e+00  17.616  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4034 on 6721 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.565e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1   6721     1093.8                               
## 2   6720     1089.7  1 4.1771   25.76 3.97e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 70109.75
## 2    3a 70086.01
## 3    3b 70071.49
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.009e-01  1.514e-01   2.647  0.00814 ** 
## phi   2.559e-02  5.598e-03   4.571 4.95e-06 ***
## alpha 8.209e-01  2.250e-02  36.484  < 2e-16 ***
## A     2.448e+02  1.610e+01  15.206  < 2e-16 ***
## k     7.243e+01  6.842e+00  10.586  < 2e-16 ***
## s     1.285e+00  4.927e-02  26.085  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4022 on 6720 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.91e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 239 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 239 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 105 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8029     1308.9                                
## 2   8028     1293.3  1 15.649  97.144 < 2.2e-16 ***
## 3   8027     1209.8  1 83.468 553.804 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 88720.87
## 2     2 88626.26
## 3     3 88092.39

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.94893    0.12701   7.471 8.78e-14 ***
## phi    -0.04165    0.00415 -10.035  < 2e-16 ***
## alpha   0.84742    0.03405  24.887  < 2e-16 ***
## A     247.98550    7.87553  31.488  < 2e-16 ***
## k      56.74056    2.30892  24.575  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3882 on 8027 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.567e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   8027     1209.8                               
## 2   8026     1209.8  1  0.0293   0.1946 0.6591    
## 3   8026     1203.1  0  0.0000                    
## 4   8025     1176.4  1 26.6548 181.8236 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 88092.39
## 2    3a 88094.20
## 3    3b 88049.73
## 4    3c 87871.78

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.105617   0.132922   8.318   <2e-16 ***
## phi    -0.040438   0.004079  -9.915   <2e-16 ***
## alpha   0.845599   0.031498  26.846   <2e-16 ***
## A     155.445661   4.473193  34.750   <2e-16 ***
## k      38.721092   0.820010  47.220   <2e-16 ***
## p       0.256607   0.014195  18.077   <2e-16 ***
## s       2.984550   0.182924  16.316   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3829 on 8025 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.026e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 281 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 281 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 55 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    879    117.885                                 
## 2    878    114.794  1  3.0906  23.638 1.377e-06 ***
## 3    877     99.686  1 15.1085 132.919 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8959.561
## 2     2 8938.129
## 3     3 8815.663

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.59246    0.22382  -2.647  0.00827 ** 
## phi     0.07663    0.01799   4.260 2.27e-05 ***
## alpha   0.89078    0.07113  12.523  < 2e-16 ***
## A     313.66069   35.61950   8.806  < 2e-16 ***
## k      90.94404   14.60378   6.227 7.35e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3371 on 877 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.364e-07
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    877     99.686                          
## 2    876     99.627  1 0.05894  0.5182 0.4718
##   model      AIC
## 1     3 8815.663
## 2    3a 8817.141
## 3    3b 8817.619
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.59246    0.22382  -2.647  0.00827 ** 
## phi     0.07663    0.01799   4.260 2.27e-05 ***
## alpha   0.89078    0.07113  12.523  < 2e-16 ***
## A     313.66069   35.61950   8.806  < 2e-16 ***
## k      90.94404   14.60378   6.227 7.35e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3371 on 877 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.364e-07
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96684, p-value = 2.824e-13
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.825, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 12 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 12 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 20 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1    984     217.32                              
## 2    983     217.06  1  0.2618  1.1857 0.2765    
## 3    982     201.70  1 15.3596 74.7812 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 10199.92
## 2     2 10200.73
## 3     3 10130.29

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    5.339e-01  5.387e-01   0.991    0.322    
## phi   7.847e-03  2.238e-02   0.351    0.726    
## alpha 7.571e-01  8.138e-02   9.303  < 2e-16 ***
## A     2.705e+02  4.192e+01   6.454 1.71e-10 ***
## k     1.134e+02  1.838e+01   6.171 9.94e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4532 on 982 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.112e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    982     201.70                          
## 2    981     201.22  1 0.47469  2.3142 0.1285
## 3    981     201.36  0 0.00000               
## 4    980     201.13  1 0.22138  1.0786 0.2993
##   model      AIC
## 1     3 10130.29
## 2    3a 10129.97
## 3    3b 10130.62
## 4    3c 10131.54

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.48861    0.52896   0.924  0.35586    
## phi     0.00759    0.02242   0.338  0.73507    
## alpha   0.75459    0.07890   9.563  < 2e-16 ***
## A     367.93804  120.22982   3.060  0.00227 ** 
## k     188.46256   85.11530   2.214  0.02704 *  
## p       0.01754    0.00731   2.399  0.01661 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4529 on 981 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.461e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96238, p-value = 2.899e-15
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.314, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 25 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 25 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 33 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   3174     1936.4                              
## 2   3173     1936.2  1   0.271  0.4434 0.5055    
## 3   3150     1809.7 23 126.501  9.5737 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 42013.68
## 2     2 42015.23
## 3     3 41577.57

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -2.300e-01  4.840e-01  -0.475    0.635    
## phi   -1.041e-03  1.522e-02  -0.068    0.945    
## alpha  1.073e+00  6.863e-02  15.633  < 2e-16 ***
## A      1.031e+03  1.551e+02   6.644 3.59e-11 ***
## k      2.895e+02  2.633e+01  10.996  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.758 on 3150 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.361e-06
##   (24 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   3150     1809.7                                 
## 2   3149     1793.2  1 16.4951 28.9671 7.901e-08 ***
## 3   3148     1791.5  1  1.6379  2.8781   0.08989 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 41577.57
## 2    3a 41550.68
## 3    3b       NA
## 4    3c 41549.80

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.149633   0.499594  -0.300    0.765    
## phi    -0.006973   0.015165  -0.460    0.646    
## alpha   1.102278   0.068901  15.998  < 2e-16 ***
## A     679.844800 117.771389   5.773 8.57e-09 ***
## k     134.180867  20.797311   6.452 1.27e-10 ***
## p      -0.012245   0.024633  -0.497    0.619    
## s       1.254117   0.166550   7.530 6.59e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7544 on 3148 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.839e-06
##   (24 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95131, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -16.973, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 130 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 130 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 622 row(s) containing missing values (geom_path).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq  F value    Pr(>F)    
## 1   1954    1003.49                                 
## 2   1953     928.39  1 75.104 157.9917 < 2.2e-16 ***
## 3   1937     895.74 16 32.646   4.4121 1.178e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24765.12
## 2     2 24614.88
## 3     3 24399.53

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.05559    0.59327   0.094    0.925    
## phi     0.18837    0.01197  15.737  < 2e-16 ***
## alpha   0.71395    0.08936   7.990 2.29e-15 ***
## A     650.60407  109.71876   5.930 3.58e-09 ***
## k     149.00776   17.04266   8.743  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.68 on 1937 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.68e-06
##   (21 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1937     895.74                          
## 2   1936     894.84  1 0.90602  1.9602 0.1617
## 3   1936     895.20  0 0.00000               
## 4   1935     894.82  1 0.38442  0.8313 0.3620
##   model      AIC
## 1     3 24399.53
## 2    3a 24399.57
## 3    3b 24400.35
## 4    3c 24401.52

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.05559    0.59327   0.094    0.925    
## phi     0.18837    0.01197  15.737  < 2e-16 ***
## alpha   0.71395    0.08936   7.990 2.29e-15 ***
## A     650.60407  109.71876   5.930 3.58e-09 ***
## k     149.00776   17.04266   8.743  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.68 on 1937 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.68e-06
##   (21 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91719, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.1622, p-value = 0.001566
## alternative hypothesis: two.sided

predict and plot

## Warning in mean.default(G_M261$MEASTIM, na.rm = TE): argument is not numeric or
## logical: returning NA

## Warning: Removed 78 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 78 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1000 row(s) containing missing values (geom_path).

plotting 2

## Warning: Removed 20 rows containing missing values (geom_point).

## Warning: Removed 20 rows containing missing values (geom_pointrange).

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    358     116.29                                
## 2    357     114.91  1 1.3849  4.3026   0.03877 *  
## 3    356     109.97  1 4.9388 15.9884 7.752e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3786.810
## 2     2 3784.485
## 3     3 3770.626

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.91698    0.31202  -6.144 2.16e-09 ***
## phi     0.04519    0.02501   1.807   0.0716 .  
## alpha   0.55854    0.12896   4.331 1.93e-05 ***
## A     784.22760  358.77095   2.186   0.0295 *  
## k     309.03977  174.58871   1.770   0.0776 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5558 on 356 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.244e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    356     109.97                             
## 2    355     108.97  1 0.99453  3.2399 0.07271 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 3770.626
## 2    3a 3769.346
## 3    3b       NA
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      -1.92511    0.30822  -6.246 1.20e-09 ***
## phi      0.04613    0.02473   1.865    0.063 .  
## alpha    0.56240    0.12712   4.424 1.29e-05 ***
## A     1370.33739 1598.54510   0.857    0.392    
## k      723.17375 1016.90722   0.711    0.477    
## p        0.02058    0.01912   1.076    0.283    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.554 on 355 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 7.574e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94617, p-value = 3.48e-10
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.42121, p-value = 0.6736
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 12 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 12 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 112 row(s) containing missing values (geom_path).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   1693     593.44                              
## 2   1692     593.19  1  0.257   0.7328 0.3921    
## 3   1691     541.23  1 51.954 162.3234 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 17724.61
## 2     2 17725.88
## 3     3 17572.42

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.04086    0.30450  -3.418 0.000645 ***
## phi     0.01372    0.01182   1.161 0.245733    
## alpha   0.63633    0.04365  14.577  < 2e-16 ***
## A     282.79695   36.11588   7.830 8.53e-15 ***
## k     118.27243   12.83924   9.212  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5657 on 1691 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.307e-06
##   (15 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Warning in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M331, : No starting values specified for some parameters.
## Initializing 'ge', 'phi', 'p', 'A', 's', 'k' to '1.'.
## Consider specifying 'start' or using a selfStart model

## Error in model.frame.default(formula = ~B_plt_t2_MgHa + MEASTIME_t2 +  : 
##   variable lengths differ (found for '(sstart)')
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1691     541.23                                
## 2   1690     535.69  1  5.547    17.5 3.021e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 17572.42
## 2    3a 17556.95
## 3    3b 17566.65
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -1.037446   0.303163  -3.422 0.000636 ***
## phi     0.013711   0.011771   1.165 0.244266    
## alpha   0.642684   0.042087  15.270  < 2e-16 ***
## A     362.891231  62.540663   5.802 7.79e-09 ***
## k     216.003260  50.875228   4.246 2.30e-05 ***
## p       0.048027   0.008704   5.518 3.96e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.563 on 1690 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.641e-06
##   (15 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92789, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.6876, p-value = 1.289e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 65 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 65 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 407 row(s) containing missing values (geom_path).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2643     1183.5                                
## 2   2642     1180.0  1  3.523  7.8876  0.005014 ** 
## 3   2619     1115.4 23 64.675  6.6028 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28925.26
## 2     2 28919.37
## 3     3 28591.03

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.74057    0.77386   0.957  0.33867    
## phi     0.03712    0.01378   2.694  0.00711 ** 
## alpha   0.62727    0.05021  12.492  < 2e-16 ***
## A     199.15587   36.23088   5.497 4.24e-08 ***
## k     115.83174   10.56968  10.959  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6526 on 2619 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.738e-07
##   (25 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2619     1115.4                                
## 2   2618     1104.2  1 11.112  26.344 3.066e-07 ***
## 3   2618     1112.9  0  0.000                      
## 4   2617     1080.5  1 32.414  78.508 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 28591.03
## 2    3a 28566.76
## 3    3b 28587.30
## 4    3c 28511.74

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.74782    0.76646   0.976  0.32931    
## phi     0.03894    0.01345   2.896  0.00382 ** 
## alpha   0.62878    0.04666  13.475  < 2e-16 ***
## A     134.23475   24.50300   5.478  4.7e-08 ***
## k      79.39320    4.61436  17.206  < 2e-16 ***
## p       0.18835    0.01795  10.490  < 2e-16 ***
## s       2.52294    0.30264   8.336  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6426 on 2617 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.696e-06
##   (25 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89951, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.7174, p-value = 2.389e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 89 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 89 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 223 row(s) containing missing values (geom_path).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   1667     711.48                              
## 2   1666     709.28  1  2.201   5.1702 0.0231 *  
## 3   1665     664.47  1 44.805 112.2688 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18878.73
## 2     2 18875.56
## 3     3 18768.58

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      2.31310    1.96054   1.180  0.23824    
## phi     0.03559    0.01818   1.958  0.05039 .  
## alpha   0.72328    0.06166  11.731  < 2e-16 ***
## A     245.20104   81.52998   3.007  0.00267 ** 
## k     174.51672   20.41966   8.547  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6317 on 1665 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.028e-06
##   (5 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1665     664.47                           
## 2   1664     664.44  1 0.036384  0.0911 0.7628
##   model      AIC
## 1     3 18768.58
## 2    3a 18770.49
## 3    3b       NA
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      2.31310    1.96054   1.180  0.23824    
## phi     0.03559    0.01818   1.958  0.05039 .  
## alpha   0.72328    0.06166  11.731  < 2e-16 ***
## A     245.20104   81.52998   3.007  0.00267 ** 
## k     174.51672   20.41966   8.547  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6317 on 1665 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.028e-06
##   (5 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93428, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.4397, p-value = 9.009e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 65 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 65 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 140 row(s) containing missing values (geom_path).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    358     148.13                                
## 2    357     146.78  1  1.348  3.2785   0.07103 .  
## 3    356     127.34  1 19.443 54.3543 1.183e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3620.044
## 2     2 3618.744
## 3     3 3569.450

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -1.020903   0.487042  -2.096  0.03678 *  
## phi     0.005339   0.031246   0.171  0.86442    
## alpha   0.798409   0.093619   8.528 4.31e-16 ***
## A     148.459436  27.544549   5.390 1.29e-07 ***
## k      64.984251  20.289617   3.203  0.00148 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5981 on 356 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.243e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    356     127.34                            
## 2    355     127.34  1 0.0016481  0.0046 0.9460
## 3    355     127.33  0 0.0000000               
## 4    354     127.31  1 0.0237205  0.0660 0.7975
##   model      AIC
## 1     3 3569.450
## 2    3a 3571.445
## 3    3b 3571.418
## 4    3c 3573.351

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -1.020903   0.487042  -2.096  0.03678 *  
## phi     0.005339   0.031246   0.171  0.86442    
## alpha   0.798409   0.093619   8.528 4.31e-16 ***
## A     148.459436  27.544549   5.390 1.29e-07 ***
## k      64.984251  20.289617   3.203  0.00148 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5981 on 356 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.243e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94118, p-value = 9.029e-11
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.8532, p-value = 7.223e-12
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 13 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 13 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 53 row(s) containing missing values (geom_path).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    209     70.054                                
## 2    208     70.043  1 0.0107  0.0319    0.8585    
## 3    207     65.000  1 5.0433 16.0610 8.556e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2102.107
## 2     2 2104.074
## 3     3 2090.232

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.84715    0.39893  -4.630 6.44e-06 ***
## phi    -0.03461    0.06344  -0.546 0.585921    
## alpha   0.54693    0.11868   4.608 7.09e-06 ***
## A     251.83461   60.50467   4.162 4.62e-05 ***
## k     100.94261   28.20086   3.579 0.000429 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5604 on 207 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.946e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    207     65.000                         
## 2    206     64.857  1  0.143  0.4542 0.5011
##   model      AIC
## 1     3 2090.232
## 2    3a 2091.765
## 3    3b 2092.003
## 4    3c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.84715    0.39893  -4.630 6.44e-06 ***
## phi    -0.03461    0.06344  -0.546 0.585921    
## alpha   0.54693    0.11868   4.608 7.09e-06 ***
## A     251.83461   60.50467   4.162 4.62e-05 ***
## k     100.94261   28.20086   3.579 0.000429 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5604 on 207 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.946e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93477, p-value = 3.981e-08
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.8139, p-value = 0.06969
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 9 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 9 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 102 row(s) containing missing values (geom_path).

plotting 2

Fitted parameters

Best / selected models by ecoprovince

Code	Ecoregion	Sel.Mod
211	Northeastern Mixed Forest	3a
212	Laurentian Mixed Forest	3a
221	Eastern Broadleaf Forest	3b
222	Midwest Broadleaf Forest	3a
223	Central Interior Broadleaf Forest	3b
231	Southeastern Mixed Forest	3c
232	Outer Coastal Plain Mixed Forest	3c
234	Lower Mississippi Riverine Forest	3a
242	Pacific Lowland Mixed Forest	NA
251	Prairie Parkland (Temperate)	3b
255	Prairie Parkland (Subtropical)	3b
261	California Coastal Chaparral Forest and Shrub	1
262	California Dry Steppe	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	3
313	Colorado Plateau Semi-Desert	1
315	Southwest Plateau and Plains Dry Steppe and Shrub	NA
321	Chihuahuan Semi-Desert	NA
322	American Semidesert and Desert	NA
331	Great Plains/Palouse Dry Steppe	3
332	Great Plains Steppe	3
341	Intermountain Semi-Desert and Desert	NA
342	Intermountain Semi-Desert	3a
411	Everglades	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	3b
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	3c
M223	Ozark Broadleaf Forest Meadow	3
M231	Ouachita Mixed Forest	3a
M242	Cascade Mixed Forest	3c
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	3
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	3a
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	3a
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	3c
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	3
M334	Black Hills Coniferous Forest	3
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	3

table by ecoprovince

Code	Ecoregion	region	n.obs	n.plots	ge	ge.2.5	ge.97.5	phi	phi.2.5	phi.97.5	alpha	alpha.2.5	alpha.97.5	A	A.2.5	A.97.5	k	k.2.5	k.97.5
211	Northeastern Mixed Forest	east	6806	2847	0.4371575	0.0461307	0.8281844	0.0099476	-0.0025514	0.0224466	0.8524407	0.7981315	0.9067499	468.94445	360.257205	577.63169	219.476246	145.923219	293.02927
212	Laurentian Mixed Forest	east	18775	8891	0.3065028	0.0938863	0.5191194	-0.0014397	-0.0086404	0.0057611	0.7214615	0.6787055	0.7642176	220.08251	200.844301	239.32071	112.272660	96.915095	127.63023
221	Eastern Broadleaf Forest	east	7170	3490	0.2301082	-0.0225361	0.4827525	-0.0036112	-0.0126217	0.0053992	0.8410618	0.7885293	0.8935943	307.33549	264.280478	350.39050	68.630153	54.805106	82.45520
222	Midwest Broadleaf Forest	east	4877	2401	-0.0867262	-0.4859237	0.3124713	0.0210147	0.0022319	0.0397975	0.8854431	0.8026266	0.9682596	396.33948	313.733304	478.94566	150.640293	105.430043	195.85054
223	Central Interior Broadleaf Forest	east	8783	3725	0.2225534	-0.0093636	0.4544704	-0.0152826	-0.0253331	-0.0052322	0.7809661	0.7273449	0.8345873	181.12216	164.418748	197.82558	40.816766	35.581179	46.05235
231	Southeastern Mixed Forest	east	12347	5691	1.8230843	1.5213386	2.1248300	-0.0126174	-0.0211877	-0.0040471	0.7248750	0.6970294	0.7527206	136.61080	127.848973	145.37264	32.316058	30.578266	34.05385
232	Outer Coastal Plain Mixed Forest	east	12470	6101	1.0902599	0.7956249	1.3848949	0.0146627	0.0037607	0.0255647	0.7472119	0.7172430	0.7771807	151.67548	140.028686	163.32228	35.068065	32.582439	37.55369
234	Lower Mississippi Riverine Forest	east	1265	714	-0.0687997	-0.8137570	0.6761576	0.0241647	-0.0134990	0.0618284	0.7568143	0.6469309	0.8666977	914.88776	-27.253358	1857.02888	324.181993	-93.973657	742.33764
242	Pacific Lowland Mixed Forest	pacific	81	81	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
251	Prairie Parkland (Temperate)	east	1797	809	0.2306491	-0.4134437	0.8747419	-0.0010402	-0.0256571	0.0235767	0.7642603	0.6298616	0.8986590	149.64370	123.315855	175.97155	38.365093	32.472000	44.25819
255	Prairie Parkland (Subtropical)	pacific	663	293	-0.1519659	-0.9128520	0.6089201	-0.0473764	-0.0996120	0.0048592	0.8047939	0.6349630	0.9746248	122.71846	91.024638	154.41229	23.867545	16.909666	30.82542
261	California Coastal Chaparral Forest and Shrub	pacific	24	24	-2.7256829	-3.4640155	-1.9873504	NA	NA	NA	NA	NA	NA	8572.74879	-10644.042016	27789.53960	717.133050	-1012.557949	2446.82405
262	California Dry Steppe	pacific	0	0	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	pacific	155	155	0.4502648	-2.6350178	3.5355473	-0.0368603	-0.1638641	0.0901435	0.9006637	0.4510901	1.3502372	1723.50465	233.267473	3213.74183	330.705756	140.032018	521.37949
313	Colorado Plateau Semi-Desert	interior west	215	215	-0.9053040	-2.7295824	0.9189744	NA	NA	NA	NA	NA	NA	293.73351	59.768000	527.69902	168.829282	22.480133	315.17843
315	Southwest Plateau and Plains Dry Steppe and Shrub	interior west	4	4	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
321	Chihuahuan Semi-Desert	interior west	9	9	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
322	American Semidesert and Desert	interior west	3	3	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
331	Great Plains/Palouse Dry Steppe	interior west	304	240	5.5764039	-6.5003964	17.6532042	-0.1157279	-0.1561570	-0.0752988	0.4605733	-0.0182672	0.9394138	35.68667	-9.352018	80.72536	23.385902	4.496632	42.27517
332	Great Plains Steppe	interior west	195	106	0.3544169	-3.2024025	3.9112362	0.0109591	-0.0928977	0.1148159	0.7323201	0.1595394	1.3051009	280.40101	-122.951818	683.75385	166.979849	-110.571404	444.53110
341	Intermountain Semi-Desert and Desert	interior west	62	62	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
342	Intermountain Semi-Desert	interior west	121	120	-1.0525367	-4.8374009	2.7323276	-0.0098922	-0.1732311	0.1534468	0.5592955	-0.0121371	1.1307280	68.81187	-24.134919	161.75866	-8.039455	-10.657199	-5.42171
411	Everglades	east	93	61	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	east	6729	2989	0.4008521	0.1040018	0.6977023	0.0255848	0.0146118	0.0365578	0.8209380	0.7768288	0.8650472	244.84791	213.282676	276.41314	72.428643	59.016182	85.84110
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	east	8034	3700	1.1056172	0.8450554	1.3661791	-0.0404385	-0.0484334	-0.0324435	0.8455988	0.7838538	0.9073437	155.44566	146.677041	164.21428	38.721092	37.113658	40.32852
M223	Ozark Broadleaf Forest Meadow	east	883	343	-0.5924572	-1.0317420	-0.1531724	0.0766302	0.0413231	0.1119373	0.8907842	0.7511780	1.0303903	313.66069	243.751262	383.57012	90.944037	62.281589	119.60648
M231	Ouachita Mixed Forest	east	988	481	0.4886076	-0.5494169	1.5266321	0.0075901	-0.0364130	0.0515932	0.7545905	0.5997496	0.9094315	367.93804	132.000820	603.87525	188.462564	21.433573	355.49155
M242	Cascade Mixed Forest	pacific	3179	3176	-0.1496328	-1.1291959	0.8299303	-0.0069729	-0.0367080	0.0227623	1.1022779	0.9671816	1.2373742	679.84480	448.928334	910.76126	134.180868	93.403209	174.95853
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	pacific	1963	1963	0.0555897	-1.1079232	1.2191027	0.1883667	0.1648920	0.2118414	0.7139495	0.5387062	0.8891927	650.60407	435.424800	865.78334	149.007758	115.583882	182.43163
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	interior west	19	19	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	362	362	-1.9251098	-2.5312721	-1.3189476	0.0461314	-0.0025125	0.0947753	0.5624000	0.3123993	0.8124008	1370.33739	-1773.471530	4514.14631	723.173749	-1276.746049	2723.09355
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	1711	1711	-1.0374461	-1.6320611	-0.4428311	0.0137112	-0.0093767	0.0367992	0.6426835	0.5601352	0.7252318	362.89123	240.225933	485.55653	216.003260	116.218180	315.78834
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	2649	2648	0.7478240	-0.7551014	2.2507495	0.0389391	0.0125700	0.0653082	0.6287834	0.5372856	0.7202812	134.23475	86.187536	182.28195	79.393196	70.345035	88.44136
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	1675	1675	2.3131038	-1.5322881	6.1584956	0.0355912	-0.0000601	0.0712426	0.7232759	0.6023455	0.8442063	245.20104	85.288963	405.11312	174.516721	134.465815	214.56763
M334	Black Hills Coniferous Forest	interior west	362	170	-1.0209034	-1.9787446	-0.0630621	0.0053394	-0.0561113	0.0667901	0.7984092	0.6142943	0.9825241	148.45944	94.288949	202.62992	64.984251	25.081675	104.88683
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	interior west	213	213	-1.8471475	-2.6336277	-1.0606673	-0.0346124	-0.1596797	0.0904549	0.5469294	0.3129474	0.7809115	251.83461	132.550233	371.11899	100.942609	45.344890	156.54033

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map #2

plot phi (effect of DeltaPDSI)

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 10 rows containing missing values (geom_point).

plot k (stand age at half biomass asymptote)

## Warning: Removed 8 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US   0.5648211
## 2       pacific  -0.0713743
## 3          east   0.6599584
## 4 interior west   0.5121994

phi (effect of DeltaPDSI)

##          region  weighted.phi
## 1     entire US  0.0087208848
## 2       pacific  0.0576288559
## 3          east -0.0003007545
## 4 interior west  0.0223131748

alpha (biomass compensation effect)

##          region weighted.alpha
## 1     entire US      0.7725505
## 2       pacific      0.9272180
## 3          east      0.7789555
## 4 interior west      0.6202502

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   289.7046
## 2       pacific   693.1076
## 3          east   238.1320
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US   99.78948
## 2       pacific  139.51589
## 3          east   83.28670
## 4 interior west  162.11636

FIA - NLS Models: Biomass vs. Stand Age, G-Reconciled

JAH

2022-10-14

Background

211 - Northeastern Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

summary

model selection 2